You really have to be careful with that Euphorbia (and Euphorbias in general) if those are your growing preferences... just to emphasize the potential danger of the white sap they exude under pressure when their skin is broken.
That E. polygona makes offsets mostly around the base, right above soil level, and they are firmly anchored to the mother plant by a pretty thick umbilical cord. Only after they are fairly large (half the diameter of the mother plant or more) do they start to lose this connection and depend on their own roots. So you basically have to go in there with a blade or scissors to remove them.
And that's not terribly difficult when you can unpot the plant and go at it from below (and I do it to most of my polygonas on a fairly regular basis) but it's not going to be simple from above in a well populated community pot. The body of the offset is in the way of the umbilical cord you need to sever. Twisting and yanking is likely to send Euphorbia juice flying in every direction.
Not to discourage anybody's personal approach, this is just fair warning based on my own experience. Those Euphorbias are not so easy to separate, and they have the potential to fill a pretty big pot on their own. Wear gloves, use sharp instruments, and it's probably best to wear eye protection as well.
The sap is much less dangerous when it is not fresh. So if and when the time comes, give the plant 5 or 10 minutes to stop oozing juice before you proceed. Any cuttings you'd like to start should be handled with the same precaution until days have passed and the juice has dried.
